Structures and Bonding of the Sandwich Complexes [Ti (η5-E5) 2] 2-(E

Quantum chemical calculations using gradient-corrected DFT at the BP86/TZ2P level of the compounds [Ti(η5-. E5)2]2- (E ) CH, N, P, As, Sb) are report...
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Inorg. Chem. 2003, 42, 2504−2511

Structures and Bonding of the Sandwich Complexes [Ti(η5-E5)2]2(E ) CH, N, P, As, Sb): A Theoretical Study† Matthias Lein, Jan Frunzke, and Gernot Frenking* Fachbereich Chemie, Philipps-UniVersita¨ t Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany Received October 2, 2002

Quantum chemical calculations using gradient-corrected DFT at the BP86/TZ2P level of the compounds [Ti(η5E5)2]2- (E ) CH, N, P, As, Sb) are reported. The nature of the metal−ligand bonding has been analyzed with an energy decomposition method, and the results are compared with [Fe(η5-E5)2]. The bonding in both series of complexes is more covalent than electrostatic. The energy decomposition analysis shows that the dominant orbital interactions in the negatively charged titanium species come from the (e2′) Ti f [(η5-E5)2]2- back-donation (δ bonding) while the covalent bonding in the iron complexes come mainly from (e1′′) (Cp-)2 f Fe2+ donation (π bonding). The nature of the metal−ligand interactions does not change very much for different ligands cyc-E5 within the two series of compounds. The calculated bond dissociation energies for breaking one metal−ligand bond of the molecules [Ti(η5-E5)2]2- shows for E the order P > As > Sb . N . CH. The central message of this work is that the complexes [Ti(η5-E5)2]2- are δ bonded molecules.

Introduction The recent synthesis and X-ray structure analysis of the first homoleptic sandwich complex with a pentaphospholyl ligand, [Ti(η5-P5)2]2-, which was reported by Urne´zˇius et al.,1 has given a new impetus to the versatile chemistry of metallocenes.2 Transition metal (TM) complexes with one η5-bonded group-15 ligand cyclo-E5 (E ) P, As) are known since the pioneering work of Scherer,3 but all attempts to isolate homoleptic species [TM(η5-E5)2] were not successful prior to this work. Recently, theoretical studies were published by us which focused on metallocenes with π-heterocyclic ligands.4,5 The isoelectronic nitrogen analogue of ferrocene, i.e., [Fe(η5-N5)2], was predicted to be an energy* To whom correspondence should be addressed. E-mail: frenking@ chemie.uni-marburg.de. † Theoretical Studies of Inorganic Compounds. 25. Part 24: Lein, M.; Frunzke, J.; Frenking, G. Structure and Bonding, in print. (1) Urne´z´ius, E.; Brennessel, W. W.; Cramer, C. J.; Ellis, J. E.; Schleyer, P. v. R. Science 2002, 295, 832. (2) Togni, A., Haltermann, R. L., Eds. Metallocenes; Wiley-VCH: New York, 1998. (3) (a) Scherer, O. J.; Schwalb, J.; Wolmersha¨user, G.; Kaim, W.; Gross, R. Angew. Chem. 1986, 98, 346; Angew. Chem., Int. Ed. Engl. 1986, 25, 363. (b) Scherer, O. J.; Bru¨ck, T. Angew. Chem. 1987, 99, 59; Angew. Chem., Int. Ed. Engl. 1987, 26, 59. (c) Scherer, O. J.; Bru¨ck, T.; Wolmersha¨user, G. Chem. Ber. 1988, 121, 935. (d) Scherer, O. J.; Blath, C.; Wolmersha¨user, G. J. Organomet. Chem. 1990, 387, C21. (4) Lein, M.; Frunzke, J.; Timoshkin, A.; Frenking, G. Chem.sEur. J. 2001, 7, 4155. (5) Frunzke, J.; Lein, M.; Frenking, G. Organometallics 2002, 21, 3351.

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rich but kinetically stable compound.4 This work was recently extended to the heavier group-15 analogues [Fe(η5-E5)2] and [FeCp(η5-E5)] (E ) P, As, Sb).5 It was shown that the Fe(η5-E5) bonding energies have the largest values when E ) P but also the other π-heterocyclic complexes were predicted to be stable compounds. A bonding analysis using an energy partitioning scheme was also carried out. The calculated data were used to quantify the metal-ligand interactions in terms of covalent and electrostatic bonding and to determine the relative strength of the different orbital interactions.4,5 In this paper we report about quantum chemical DFT calculations of the title compounds [Ti(η5-E5)2]2- (E ) CH, N, P, As, Sb). The work is a continuation of our systematic studies of transition metal complexes with π-heterocyclic4,5 and other ligands.6 The goal of this project is to provide quantitative information about the nature of the chemical bond using a rigorously defined quantum chemical partitioning of the interaction energy. The results which we obtained so far in the field of transition metal4-6 and main group7 (6) (a) Diefenbach, A.; Bickelhaupt, F. M.; Frenking, G. J. Am. Chem. Soc. 2000, 122, 6449. (b) Uddin, J.; Frenking, G. J. Am. Chem. Soc. 2001, 123, 1683. (c) Chen, Y.; Frenking, G. J. Chem. Soc., Dalton Trans. 2001, 434. (d) Doerr, M.; Frenking, G. Z. Allg. Anorg. Chem. 2002, 628, 843. (e) Frenking, G.; Wichmann, K.; Fro¨hlich, N.; Grobe, J.; Golla, W.; Le Van, D.; Krebs, B.; La¨ge, M. Organometallics 2002, 21, 2921. (f) Rayo´n, V. M.; Frenking, G. Organometallics, submitted for publication.

10.1021/ic020592h CCC: $25.00

© 2003 American Chemical Society Published on Web 03/21/2003

Sandwich Complexes [Ti(η5-E5)2]2-

complexes have recently been summarized in a review.8 The focus of the present work is the strength and the nature of the Ti-(η5-E5) interactions. We were intrigued by the results of the orbital correlation analysis of [Ti(η5-P5)2]2- presented by Urne´zˇius et al.1 The authors suggest that there are critical differences between the nature of the bonding of the organic (Cp) versus inorganic (cyclo-P5) metal-ligand bonding. The ligand π orbitals of cyclo-P5 were found to be lower in energy than those of the Cp ligand. It was concluded that “Cp serves more as a donor and P5 as an acceptor”.1 Our recent theoretical studies of ferrocene and the inorganic analogues [Fe(η5-E5)2] and [FeCp(η5-E5)] have shown, however, that the Fe-(η5-E5) and Fe-Cp interactions are very similar to each other.4,5 It will be interesting to see if the suggestion of Urne´zˇius et al.,1 which was based on a qualitative orbital interaction diagram, is supported by a quantitative analysis of the bonding energy. Therefore, we calculated also [TiCp2]2- and the other members of the series [Ti(η5-E5)2]2- (E ) N, Sb, As) and we compared the results with the data for ferrocene and [Fe(η5-E5)2]. Another topic which we address in this work is the strength of the electrostatic attraction in the complexes. Urne´zˇius et al. speculated that “Our success in obtaining such a complex in the form of a charged species suggests that electrostatics may also play an important role in the stabilization of monomers containing [(P5)2M]z units”.1 We shall see that the electrostatic effects play only an indirect role for the strength of the metal-ligand bonding by raising the energy levels of the orbitals. Methods The geometries have been optimized at the gradient-corrected DFT level using the exchange functional of Becke9 and the correlation functional of Perdew10 (BP86) in conjunction with uncontracted Slater-type orbitals (STOs) as basis functions.11 Relativistic effects have been considered by the zero-order regular approximation (ZORA).12 The basis sets for titanium and iron have triple-ζ quality augmented by one set of 6p functions. Triple-ζ basis sets augmented by two sets of d-type polarization functions have been used for the main group elements. The (n - 1)s2, (n - 1)p6, and (n - 2)d10 core electrons of the main group elements and the (1s2s2p)10 core electrons of Ti and Fe were treated by the frozencore approximation.13a An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular densities and to represent the Coulomb and exchange potentials accurately in each SCF cycle.13b We calculated the vibrational frequencies of the optimized structures (7) (a) Loschen, C.; Voigt, K.; Frunzke, J.; Diefenbach, A.; Diedenhofen, M.; Frenking, G. Z. Allg. Anorg. Chem. 2002, 628, 1294. (b) Rayo´n, V. M.; Frenking, G. Chem.sEur. J. 2002, 8, 4693. (8) Frenking, G.; Wichmann, K.; Fro¨hlich, N.; Loschen, C.; Lein, M.; Frunzke, J.; Rayo´n, V. M. Coord. Chem. ReV., in press. (9) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (10) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (11) Snijders, J. G.; Baerends, E. J.; Vernooijs, P. At. Nucl. Data Tables 1982, 26, 483. (12) (a) Chang, C.; Pelissier, M.; Durand, Ph. Phys. Scr. 1986, 34, 394. (b) Heully, J.-L.; Lindgren, I.; Lindroth, E.; Lundquist, S.; MartenssonPendrill, A.-M. J. Phys. B 1986, 19, 2799. (c) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (d) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1996, 105, 6505. (e) van Lenthe, E.; van Leeuwen, R.; Baerends, E. J.; Snijders, J. G. Int. J. Quantum Chem. 1996, 57, 281.

to see if they are minima on the potential energy surface (PES). All calculations have been carried out with the program package ADF.13,14 The metal-ligand bonding interactions have been analyzed with the energy decomposition scheme of the program ADF,14,15 which is based on the EDA method of Morokuma16 and the similar ETS method of Ziegler.17 For the energy partitioning analysis the interaction energy ∆Eint of [Ti(η5-E5)2]2- with D5h symmetry was calculated and decomposed for the bonding between the metal atom with the electron configuration Ti(e2′)4 and the ligand fragment [(cyc-E5)2]2-. The energy partitiong analysis was also performed using the metal fragment TM(η5-E5)- and the ligand (η5-E5)- in the 1A1′ and 1A1 ground state, respectively. The instanteneous interaction energy ∆Eint can be divided into three components: ∆Eint ) ∆Eelstat + ∆EPauli + ∆Eorb

(1)

∆Eelstat gives the electrostatic interaction energy between the fragments which are calculated with a frozen electron density distribution in the geometry of the complex. It can be considered as an estimate of the electrostatic contribution to the bonding interactions. The second term in eq 1, ∆EPauli, gives the repulsive four-electron interactions between occupied orbitals. The last term gives the stabilizing orbital interactions, ∆Eorb, which can be considered as an estimate of the coValent contributions to the bonding. Thus, the ratio ∆Eelstat/∆Eorb indicates the electrostatic/ covalent character of the bond. The covalent term can be partitioned further into contributions by the orbitals which belong to different irreducible representations of the interacting system. This makes it possible to calculate e.g. the contributions of σ and π bonding to a covalent multiple bond.8 Technical details about the ETS method can be found in the literature.15 The bond dissociation energy (BDE) ∆Ee is given by the sum of ∆Eint and the fragment preparation energy ∆Eprep: ∆Ee ) ∆Eprep + ∆Eint

(2)

∆Eprep is the energy which is necessary to promote the fragments from their equilibrium geometry and electronic ground state to the geometry and electronic state which they have in the optimized structure.

Geometries We optimized the geometries of the complexes [Ti(η5E5)2]2- (E ) CH, N, P, As, Sb) in the electronic singlet state with staggered (D5d) and eclipsed (D5h) conformations of the cyclic ligands. The molecules have also been optimized in the electronic triplet state without symmetry constraints using structures with staggered and eclipsed conformations of the ligands as starting geometries. Table 1 gives the (13) (a) Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys. 1973, 2, 41. (b) Krijn, J.; Baerends, E. J. Fit Functions in the HFS-Method; Internal Report (in Dutch); Vrije Universiteit: Amsterdam, The Netherlands, 1984. (14) ADF99: (a) Versluis, L.; Ziegler, T. J. Chem. Phys. 1988, 322, 88. (b) te Velde, G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 84. (c) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chim. Acta 1998, 99, 391. (15) (a) Bickelhaupt, F. M.; Baerends, E. J. ReViews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; Wiley-VCH: New York, 2000; Vol. 15, p 1. (b) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (16) Morokuma, K. J. Chem. Phys. 1971, 55, 1236. (17) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1.

Inorganic Chemistry, Vol. 42, No. 8, 2003

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Lein et al. Table 1. Calculated Bond Lengths (Å) and Relative Energies (kcal/mol) of [Ti(E5)2

Complexes and Fragments at BP86/TZ2P

symmetry

state

Ti-E

Ti-Xa

E-E

ib

Erel

Ti(Cp)2 Ti(Cp)22Ti(Cp)22Ti(N5)22Ti(N5)22Ti(N5)22-

D5h D5d D5d D5h D5d C2V

1A ′ 1 1A 1g 3A 1g 1A ′ 1 1A 1g 3A 1

1.912 1.921 2.018 1.781 1.788

0.0 1.9 -27.0 0.0 0.9 24.9

D5h D5d C2V

1A ′ 1 1A 1g 3A 1

0 1 0

0.0 5.2 46.8

Ti(As5)22Ti(As5)22Ti(Sb5)22Ti(Sb5)22Ti(Cp)Ti(N5)Ti(P5)Ti(As5)Ti(Sb5)-

D5h D5d D5h D5d C5V C5V C5V C5V C5V

1A ′ 1 1A 1g 1A ′ 1 1A 1g 1A 1 1A 1 1A 1 1A 1 1A 1

1.460 1.459 1.427 1.405 1.404 1.365 1.393 1.418 2.196 2.185 2.168 2.197 2.217 2.445 2.447 2.837 2.837 1.429 1.376 2.259 2.532 2.937

c c c 0 1 0

Ti(P5)22Ti(P5)22Ti(P5)22-

2.280 2.287 2.350 2.145 2.150 2.225 2.279 2.313 2.577 2.620 2.720 2.641 2.773 2.802 2.774 3.089 3.087 2.333 2.004 2.386 2.524 2.765

0 1 0 1 0 0 0 0 0

0.0 7.6 0.0 9.0

molecule 2-

a

]2-

1.775 1.847

1.878 1.834 1.929 1.926 1.991 1.894 1.414 1.316 1.185

X is the midpoint of the E5 ring. b Number of imaginary frequencies. c SCF did not converge.

Figure 1. Calculated equilibrium geometries at BP86/TZ2P of the energetically lowest lying singlet and triplet species of [Ti(Cp)2]2- and the singlet state of [Ti(η5-P5)2]2-. Interatomic distances are given in Å.

calculated bond lengths. The equilibrium geometries of the energetically lowest lying singlet and triplet species of [Ti(Cp)2]2- and the singlet state of [Ti(η5-P5)2]2- are shown in Figure 1. The calculation of the vibrational frequencies showed that the titanium metallocene complexes [Ti(η5-E5)2]2- in the electronic singlet state which have an eclipsed (D5h) form are energy minima while the staggered (D5d) forms are transition states (i ) 1). This is in agreement with the X-ray structure analysis of [Ti(η5-P5)2]2-, which gave a geometry where the two P5 rings are eclipsed.1 The Cp rings of ferrocene have also an eclipsed conformation while the group-15 heterocyclic analogues [Fe(η5-E5)2] (E ) N, P, As, Sb) are predicted to have a staggered equilibrium geometry.4,5

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Figure 1 shows that the calculated bond lengths of [Ti(η5P5)2]2- are in very good agreement with the experimental values. The energy difference between the staggered and eclipsed conformations of [Fe(η5-E5)2] increases when the heteroatom E becomes heavier N < P < As < Sb (Table 1). The calculation of the vibrational frequencies of the parent metallocene complex [Ti(Cp)2]2- using numerical second derivatives failed because of SCF convergence problems. This may be caused by the fact that the triplet state of [Ti(Cp)2]2- is lower in energy than the singlet state. Table 1 shows that the triplet state with a staggered conformation of the Cp ligands is 27.0 kcal/mol below the lowest lying singlet state. This result is in agreement with the experimental observation that [Cr(Cp)2] which is isoelectronic with [Ti(Cp)2]2- has a triplet electronic ground state.19 The geometry optimization of triplet [Ti(Cp)2]2- was carried out without symmetry constraints, and therefore, we think that the optimized structure is a minimum on the potential energy surface. The triplet states of the heteroanalogues [Ti(η5E5)2]2- (E ) N, P) are higher in energy than the singlet states (Table 1). The triplet states of [Ti(η5-As5)2]2- and [Ti(η5Sb5)2]2- are probably also higher in energy than the singlet states and have therefore not been calculated by us. Bonding Analysis Figure 2 shows a qualitative orbital correlation diagram of the interactions between a d4 and d6 metal atom TM and a (cyc-E5)2 ligand in D5d symmetry yielding the complexes [TM(cyc-E5)2] with 16 and 18 electrons, respectively. This is the standard MO correlation diagram for ferrocene which is discussed in many textbooks.20 The difference between the correlation diagrams of a d4 and d6 metal atom is that the dz2 (a1′) AO in the latter atom is occupied while it is (18) See Figure 2 in ref 1. (19) Elschenbroich, Ch.; Salzer, A. Organometallics, 2nd ed.; VCH: Weinheim, Germany, 1992.

Sandwich Complexes [Ti(η5-E5)2]2-

Figure 2. Qualitative orbital correlation diagram of the interactions between a d4 and d6 metal atom TM and a (cyc-E5)22- ligand in D5h symmetry. The dz2(a1′) AO of TM(d4) and, thus, the highest lying 2a1′ MO of a 16 electron complex [TM(η5-E5)] are empty. The symmetry assignments σ, π, and δ refer to the metal-ligand bonds in the complex.

empty in the former atom. This means that the 2a1′ MO of [TM(cyc-E5)2] is empty in the 16 electron complex. There is general agreement that the most important orbital interactions in ferrocene arise from the (e1′′) (Cp-)2 f Fe2+ donation.21 Our quantitative analysis of the metal-ligand bonding in [FeCp2] and [Fe(η5-N5)2] with D5d symmetry showed that the e1g donation, which is equivalent to e1′′ donation in D5h symmetry, contributes with ∼65% to the (20) (a) Reference 19, page 320. (b) Albright, T. A.; Burdett, J. K.; Whangbo, M. H. Orbital Interactions in Chemistry; Wiley: New York, 1985; p 393. (b) Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. AdVanced Inorganic Chemistry, 6th ed.; John Wiley: New York, 1999; p 686.

total orbital interactions.4,21 In the paper by Urne´zˇius et al.1 it was argued that the π orbitals of cyc-P5 are energetically lower lying than those of Cp and, therefore, the strongest metal-ligand interactions in the 16 electron complex [Ti(η5-P5)2]2- would take place between the e2′ orbital set of the metal and the ligand (energy matching).18 This means that the strongest donor-acceptor interactions in the latter complex should come from the (e2′) Ti f [(η5-P5)2]2- backdonation. Since e2′ symmetry is equivalent to δ bonding and e1′′ symmetry is equivalent to π bonding, the above conclusion would mean that [Ti(η5-P5)2]2- is a δ bonded molecule and ferrocene is a π bonded molecule. Inorganic Chemistry, Vol. 42, No. 8, 2003

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Lein et al. Table 2. Energy Decomposition Analysis of kcal/mol

[Ti(η5-E5)2]2-

in D5h Symmetry Using the Fragments

Ti(e2′)4

and

[(cyc-E5)2]2-

with Energy Values in

term

E ) CH

E)N

E)P

E ) As

E ) Sb

∆Eint ∆EPauli ∆Eelstata ∆Eorba A1′b (σ) A2′ E1′b (π) E2′b (δ) A1′′ A2′′b (σ) E1′′b (π) E2′′b (δ) s p d

-238.7 204.9 -141.9 (32.0) -301.6 (68.0) -10.2 (3.4) 0.00 -4.7 (1.6) -231.7 (76.8) 0.00 -3.1 (1.0) -50.6 (16.8) -1.4 (0.5) -13.3 (4.4) -55.3 (18.4) -233.1(77.3% )

-255.4 257.0 -112.2 (21.9) -400.1 (78.1) -17.7 (4.4) 0.00 -4.8 (1.2) -315.0 (78.7) 0.00 -3.6 (0.9) -56.1 (14.0) -2.9 (0.7) -21.3 (5.3) -60.9 (15.2) -317.9 (79.4)

-359.7 334.7 -272.8 (39.3) -421.6 (60.7) -10.1 (2.4) 0.00 -3.7 (0.9) -358.1 (84.9) 0.00 -3.0 (0.7) -45.1 (10.7) -1.6 (0.4) -13.1 (3.1) -48.8 (11.6) -359.7 (85.3)

-349.5 240.8 -227.7 (38.6) -362.7 (61.4) -8.7 (61.4) 0.00 -3.6 (1.0) -320.2 (88.3) 0.00 -3.2 (0.9) -25.9 (7.1) -1.1 (0.3) -11.9 (3.3) -29.5 (8.1) -321.3 (88.6)

-341.3 194.7 -204.3 (38.7) -331.7 (61.3) -14.9 (61.3) 0.00 -5.2 (1.6) -286.9 (86.5) 0.00 -6.2 (1.9) -18.1 (5.5) -0.4 (0.1) -21.1 (6.4) -23.3 (7.1) -287.3 (86.6)

a The value in parentheses gives the percentage contribution to the total attractive interactions. b The value in parentheses gives the percentage contribution to the total orbital interactions.

Table 2 gives the results of the energy decomposition analysis of the complexes [Ti(η5-E5)2]2- (E ) CH, N, P, Sb, As) using symmetry-adapted orbitals from the D5h point group. The interacting fragments are Ti(e2′)4 and [(cycE5)2]2-. The same fragments were chosen by Urne´zˇius et al.1 The calculated interaction energies between the frozen fragments have large negative values which indicate strong attraction. Note that the largest value is calculated for E ) P (∆Eint ) -359.7 kcal/ mol) and that the lowest values are calculated for E ) CH (∆Eint ) -238.7 kcal/mol) and E ) N (∆Eint ) -255.4 kcal/mol). This indicates that the carbon and nitrogen complexes have the weakest metal-ligand bonds, while the bonds in the heavier heterometallocenes [Ti(η5As5)2]2- and [Ti(η5-Sb5)2]2- are only slightly weaker than in the phosphorus complex. The metal-ligand bonding between Ti(e2′)4 and [(cyc-E5)2]2- is largely covalent. The calculated data suggest that the ∆Eorb term contributes between 60.7% (E ) P) and 78.1% (E ) N) to the attractive interactions. The relatively low degree of electrostatic attraction in [Ti(η5P5)2]2- is at variance with the suggestion of Urne´zˇius et al.1 that electrostatics may play an important role in the stabilization of the complex. We want to point out that the comparatively weak bonding in [Ti(η5-N5)2]2comes from the relatively small electrostatic term (∆Eelstat ) -112.2 kcal/mol) while the orbital interactions are rather strong (∆Eorb ) -400.1 kcal/mol). The most important result given in Table 2 concerns the contributions of the orbital interactions which have different symmetry to the ∆Eorb term. The calculated data support the (21) Most textbooks discuss the orbital correlation diagram of metallocenes [TM(Cp2)] using orbitals which belong to the D5d group (staggered conformation) although the parent compound ferrocene has a D5h equilibrium geometry. The two conformations are very close in energy, and the orbital correlation diagrams are very similar except that the symmetry labels of the orbitals are different. For the purpose of comparing the results of this work with our previous study,4 we give the pairs of orbitals in D5d and D5h symmetry which correspond to each other: a1g T a1′; a2u T a2′′; e1g T e1′′; e1u T e1′; e2g T e2′; e2u T e2′′. The energy decomposition analysis of [Ti(η5-E5)2]2- and [Fe(η5-E5)2] in D5h and D5d symmetry give very similar results for the contributions of the energy terms ∆Eelstat, ∆EPauli, and ∆Eorb and for the contributions of the orbitals having a different symmetry in the latter term.

2508 Inorganic Chemistry, Vol. 42, No. 8, 2003

statement of Urne´zˇius et al.1 that the strongest metal-ligand orbital interactions in [Ti(η5-P5)2]2- come from the e2′ orbitals. The energy analysis suggests that the (e2′) Ti f [(η5-P5)2]2- back-donation contributes 84.9% to the ∆Eorb term. The e1′′ orbitals, which were found to be the most important contributors to the orbital interactions in ferrocene,4,21 contribute only 10.7% in in [Ti(η5-P5)2]2- (Table 2). It follows that the most important metal-ligand bond in [Ti(η5-P5)2]2- is indeed a δ bond. However, the energy analysis shows that the e2′ orbitals are also the most important orbitals for the ∆Eorb term of in [Ti(Cp)2]2-!22 The orbital interactions of the e2′ orbital give 76.8% of the total covalent interactions in the latter complex. This is at variance with the suggestion of Urne´zˇius et al.,1 who concluded that the difference between ferrocene and [Ti(η5-P5)2]2- is the nature of the ligand. The results in Table 2 indicate that the nature of the metal-ligand bonding in [Ti(η5-P5)2]2- is not very different from that in [Ti(Cp)2]2-. The data suggest that the different orbital interactions in [Ti(η5-P5)2]2- and [Fe(Cp)2] are rather caused by the nature of the metal and/or the charge of the complex. To prove this hypothesis we compared the results of the energy analysis of [Ti(η5-E5)2]2- with the data of [Fe(η5E5)2] (E ) CH, N, P, Sb, As) which have been published by (22) One reviewer argued that it would be invalid to assert that Cp- and P5- engage in equivalent δ bonding to titanium when [Ti(Cp)2]2- has a triplet ground state while [Ti(η5-P5)2]2- is a singlet. We want to emphasize that the goal of the analysis is to elucidate the difference of the bonding behavior between the two ligands when they bind to a metal which has the same electron configuration. The analysis of the metal-ligand bonding in triplet (3A1′) [Ti(Cp)2]2- should be carried out with the fragments (Cp-)2 and Ti with the electron configuration Ti(a1′)2(e2′)RR. A comparison of the results with the analysis of [Ti(η5-P5)2]2- given in Table 2 would would mean that the bonding to a metal which has different electron configurations is considered. This is not meaningful for the purpose of comparing the intrinsic differences between the two ligands. We want to point out that the analysis of the bonding situation in [Fe(Cp)2] and [Fe(η5-P5)2] which both have a singlet ground state showed also that the two ligands have similar bonding properties. A result, which is interesting in the context of the question which was raised by the reviewer, has been reported by us in ref 6f. There it is shown that the preference of ferrocene for π bonding is also found when the EPA is carried out with the neutral fragments Fe and Cp2 in the triplet states.

Sandwich Complexes [Ti(η5-E5)2]2-

Figure 3. Qualitative orbital correlation diagram for the interactions between cyclo-E5- and [TM(η5-E5)] in C5V symmetry. Only those orbitals which are relevant for the metal-ligand bonding are shown. The a1 MO of [TM(η5-E5)] and, thus, the 2a1 MO of 16 electron complexes [TM(η5-E5)2] are empty. The symmetry assignments σ, π, and δ refer to the metal-ligand bonds in the complex.

us before.5 The bonding analysis of the neutral iron complexes was carried out in terms of interactions between the fragments cyclo-E5- and [Fe(η5-E5)]+. A qualitative orbital correlation diagram for the interactions between cyclo-E5and [TM(η5-E5)] which shows only the orbitals which are relevant for the metal-ligand bonding is given in Figure 3. The fragment [TM(η5-E5)] has C5V symmetry, which means that there can only be orbitals which have a1, a2, e1, and e2 symmetry. There are no relevant valence orbitals in the molecules which have a2 symmetry. The σ interactions of the a1 orbitals should not lead to a significant stabilization because the a1 ligand orbital is much lower in energy than the e1 orbital. The crucial difference between the ∆Eorb term of the neutral iron complexes [Fe(η5-E5)2] and the negatively charged titanium species [Ti(η5-E5)2]2- is the strength of the e1 (π) and e2 (δ) orbital interactions. The former interactions should be strong when the orbitals of [TM(η5-E5)] are low

in energy yielding better energy matching of the e1 orbitals while the latter interactions should become stronger when the orbitals of the metal fragment are energetically high lying. Table 3 gives the results of the energy decomposition analysis of the two series of compounds. The calculated orbital contributions to the ∆Eorb term support the qualitative arguments. The largest stabilization energy of the iron complexes which have a positively charged [Fe(η5-E5)]+ metal fragment with low-lying orbitals comes always from the e1 orbitals which contribute between 63.8% and 69.4% to the total covalent bonding energy. There is a continuous increase of the relative ∆E(e1) values from [Fe(η5-Cp)2] to [Fe(η5-Sb5)2], but the differences are not very large. We want to point out that the nature of the metalligand bonding in [Fe(η5-E5)2] changes very little for different E species. The calculations suggest that the (η5-E5)-[Fe(η5-E5)]+ interactions have a slightly higher electrostatic Inorganic Chemistry, Vol. 42, No. 8, 2003

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Lein et al. [Ti(η5-E5)2]2-

Table 3. Energy Decomposition Analysis of [Fe(η5-E5)]+/(η5-E5)- with Energy Values in kcal/mol

and

[Fe(η5-E

5)2]

in C5V Symmetry Using the Fragments

Ti Term

E ) CH

E)N

E)P

[Ti(η5-E

5 5)] /(η -E5)

and

Fe E ) As

E ) Sb

E ) CH

E)N

∆Eint -30.5 -27.5 -39.5 -33.3 -29.4 -237.6 -198.0 ∆EPauli 116.7 132.7 178.5 198.2 195.1 172.4 149.7 ∆Eelstata -22.4 (15.2) -3.7 (2.3) -63.0 (28.9) -84.5 (36.5) -87.4 (38.9) -238.5 (58.2) -184.3 (53.0) ∆Eorba -124.8 (84.8) -156.5 (97.7) -154.9 (71.1) -147.0 (63.5) -137.2 (61.1) -171.5 (41.8) -163.4 (47.0) A1b (σ) -8.5 (6.8) -12.7 (8.1) -16.5 (10.7) -18.9 (12.9) -25.5 (18.6) -25.0 (14.6) -22.4 (13.7) A2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 E1b (π) -30.6 (24.5) -34.8 (22.3) -48.8 (31.5) -49.6 (33.7) -52.0 (37.9) -109.3 (63.8) -106.1 (65.0) E2b (δ) -85.7 (68.7) -109.0 (69.6) -89.6 (57.8) -78.5 (53.4) -59.6 (43.5) -37.1 (21.6) -34.9 (21.3) ∆Eprep 83.0 44.4 27.4 27.5 30.5 2.8 13.1 ∆E ()De) 52.5 16.9 -12.1 -5.8 1.1 -234.8 -184.9

E)P

E ) As

E ) Sb

-199.5 190.2 -207.3 (53.2) -182.5 (46.8) -28.1 (15.4) 0.0 -120.7 (66.1) -33.7 (18.5) 28.0 -171.5

-183.8 221.6 -223.1 (55.0) -182.3 (45.0) -29.1 (16.0) 0.0 -123.7 (67.8) 29.6 (16.2) 23.3 -160.5

-165.1 220.8 -205.1 (53.1) -180.9 (46.9) -35.7 (19.7) 0.0 -125.6 (69.4) -19.6 (10.8) 46.3 -118.8

a The value in parentheses gives the percentage contribution to the total attractive interactions. b The value in parentheses gives the percentage contribution to the total orbital interactions.

Figure 4. Plot of the highest lying occupied e2′ orbitals of (D5h) [Ti(η5-P5)2]2- and [Fe(η5-P5)2]: (a) HOMO of [Ti(η5-P5)2]2-; (b) HOMO-3 of [Fe(η5P5)2].

(53.2-58.2%) than covalent character. The lowest degree of covalent bonding is calculated for ferrocene. The energy decomposition results for the titanium complexes [Ti(η5-E5)2]2- differ significantly from those of [Fe(η5-E5)2]. Table 3 shows that the covalent bonding term ∆Eorb is much larger than ∆Eelstat for all titanium complexes. In the nitrogen complex [Ti(η5-N5)2]2-, the calculations indicate that the (η5-N5)--[Ti(η5-N5)]- interactions are nearly exclusively covalent. Thus, the electrostatic attractions play a larger role for the stabilization of the neutral complexes [Fe(η5-E5)2] than in [Ti(η5-E5)2]2-. It may be argued that the higher degree of electrostatic metal-ligand bonding in the former compounds comes from the choice of the fragments [Fe(η5-E5)]+ and (η5-E5)- which have opposite charges that could lead to large values for the charge attraction. However, a recent energy partitioning analysis of the metal-ligand bonding in ferrocene using neutral fragments Fe and Cp in the triplet states and charged fragments Fe2+ and Cp- in the singlet state showed that the relative contributions of ∆Eelstat and ∆Eorb change very little.6f It has been shown earlier by us that the charge of the fragments has a very strong influence of the energy levels of the orbitals which in turn may even enhance the orbital interactions more than the electrostatic interactions.6a A second difference between the neutral iron complexes and the charged titanium species concerns the most important orbital term. Table 3 shows that the largest contribution to ∆Eorb comes always from the e2 orbitals, i.e., from the

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electron donation of the HOMO of [Ti(η5-E5)2]- to the LUMO of (η5-E5)-. The latter orbital interaction is always stronger than the e1 term, although the ∆E(e2) contribution to the total orbital interaction energy decreases from 69.6% in [Ti(η5-N5)2]2- to 43.5% in [Ti(η5-Sb5)2]2- while the ∆E(e1) contribution increases from 22.3% to 37.9%. The contributions of the a2 orbitals are always less than the e1 and e2 values. Thus, the most important metal-ligand bonds in [Ti(η5-E5)2]2- are δ bonds while the metal-ligand bonds in [Fe(η5-E5)2] have π symmetry. The large contribution of the metal-ligand δ bonding in in [Ti(η5-E5)2]2- is also revealed by the shape of the occupied orbitals. Figure 4a shows a plot of the e2′ HOMO of [Ti(η5-P5)2]2-. There is a large overlap between the d(e2′) AO of the metal and the π orbitals of the ring. Figure 4b gives for comparison the corresponding e2′ orbital of [Fe(η5-P5)2] which is the HOMO-3. It becomes obvious that the latter MO is mainly a metal lone-pair orbital without large contributions of the ligand π orbitals. This is supported by the mixing coefficients of the fragment orbitals which is given by the ETS method. The contribution of the d(e2′) AO of Ti to the e2′ HOMO of [Ti(η5-P5)2]2- is 33.6% while 60.2% come from the valence π orbitals of P5.23 The contribution of the Fe orbitals to the HOMO-3 of [Fe(η5P5)2] is 69.0% while only 21.9% come from (P5)2. (23) Further contributions which then give 100% come from lower lying orbitals of the same symmetry.

Sandwich Complexes [Ti(η5-E5)2]2-

The calculated energy values of ∆E(e1) and ∆E(e2) of the complexes [Ti(η5-P5)2]2- and [Fe(η5-Cp)2] thus agree with the suggestion of Urne´zˇius et al.1 that the inorganic ligand (η5-P5) serves as an electron acceptor in the former compound while Cp serves as an electron donor in the latter. However, the difference is not because the ligands are different. The difference comes from the fact that the titanium complex carries two negative charges while ferrocene is a neutral compound. Finally we want to comment on the relative stabilities of the [Ti(η5-E5)2]2- series for different E species which are predicted by the calculations. We want to point out that the chemical stabilities of the complexes are strongly influenced by the counterions whose effects are not considered here. Therefore, the calculated values should be judged with caution. Nevertheless, the calculated values of the interaction energy ∆Eint and the bond dissociation energy ∆Ee ()-De) provide useful information about the trend of the intrinsic stabilities. The ∆Eint values in Table 3 indicate that the net interaction energy is only weakly stabilizing (compared with the values for [Fe(η5-E5)2]) because the attractive electrostatic and covalent forces are largely compensated by the Pauli repulsion. The ∆Eint values give a stability trend of [Ti(η5E5)2]2- with P > As > Sb > CH > N. The values of the preparation energy ∆Eprep of the heavier ligand atoms P, As, and Sb are not very different from each other, and therefore, they do not alter the predicted trend of the stability of these compounds. However, the ∆Eprep values of [Ti(η5-N5)2]2and [Ti(Cp)2]2- are much higher and, therefore, the dissociation of a ligand becomes exothermic. It should be noted that [Ti(Cp)2]2- has a triplet ground state and that the nitrogen complex [Ti(η5-N5)2]2- is thermodynamically highly unstable

because the fragmentation of the cyclic N5 ligand into N2 is highly exothermic.4 The calculated bond dissociation energies De indicate that the phosphorus and arsenic complexes are intrinsically stable with respect to dissociation of one ligand. Since the phosphorus complex [Ti(η5-P5)2]2- could be prepared, it seems possible that also the arsenic analogue [Ti(η5-As5)2]2- could be isolated while it will be difficult to synthesize [Ti(η5-Sb5)2]2-. Summary and Conclusion The energy decomposition analysis of the complexes [Ti(η5-E5)2]2- and [Fe(η5-E5)2] (E ) CH, N, P, As, Sb) shows that the metal-ligand bonding in both series of complexes is more covalent than electrostatic. The dominant orbital interactions in the negatively charged titanium species come from the (e2′) Ti f [(η5-E5)2]2- back-donation (δ bonding) while the covalent bonding in the iron complexes comes mainly from (e1′′) (Cp-)2 f Fe2+ donation (π bonding). The nature of the metal-ligand interactions does not change very much for different ligands cyc-E5 within the two series of compounds. The calculated bond dissociation energies for breaking one metal-ligand bond of the molecules [Ti(η5E5)2]2- shows for E the order P > As > Sb . N . CH. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft and by the Fonds der Chemischen Industrie. Excellent service by the Hochschulrechenzentrum of the Philipps-Universita¨t Marburg is gratefully acknowledged. Additional computer time was provided by the HLRS Stuttgart and the HLR Darmstadt. IC020592H

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